Questions tagged [wolfram-alpha]
For mathematical questions related to the usage of WolframAlpha.
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WolframAlpha syntax - evaluate series at a point
I am looking for syntax for WolframAlpha, which would evaluate a series at a given point. My goal is to have a sheet of practice exercises with links to solutions in WolframAlpha.
Example problem: ...
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Solve a 2D linear recurrence
I need to know the solution of this recurrence:
$$2a[n,k-1]-a[n-1,k-1]-2a[n-1,k-2]+a[n-2,k-2]=a[n,k]$$
With the initial value unspecified.
Also, wolfram is good at solving linear 1D recurrence, but ...
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PDF or CDF of the sum of two Weibull random variables with shape parameter 1/2
I saw that the pdf of the sum of two independent Weibull random variables is not known in general.
However, in the case of 'shape parameter = 1/2' in both variables, is there a closed-form expression ...
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How can i use Maple(or any other software) to rearrange any equation into another equation? [closed]
Let's say I have some equation $= x^2+y=3$. I want to somehow rearrange this into something else such as $x=({\rm root}(3-y) z)/z$. I solved for x and multiplied z above and below. Can Maple (or some ...
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Deriving CI for the mean: Wolfram Alpha giving different answer for equation and inequality [closed]
As a simple example, say I'm trying to derive the upper bound of a confidence interval for the mean. That is, I'm trying to solve for $\mu$ in
$$ \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}} < Z_{\...
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Wolfram Mathematica: why is the plot not visible?
simple question regarding Wolfram Mathematica:
Why is the plot not showing?
(See screenshot)
(I am new to Wolfram Mathematica)
Thankful for any input.
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Wolfram Mathematica Monte Carlo for integrals approximation
I wanted to implement the Monte Carlo method for multiple integrals approximation in Wolfram Mathematica. Namely I wanted to let the user insert as input the dimension of the integral and the number ...
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How are person curves created?
One can graph some person curves such as Joe Biden curve and Kim Jung Un Curve using WolframAlpha. I am curious how these curves were created using parametric equations.
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Discrepancy in value of $\int_0^\frac\pi2 \delta(\tan(t)-xt)dt$
The goal would have been for the smallest positive solution of $y\cot(y)=x$ using a Dirac $\delta(x)$ Fourier series and the Bateman function:
$$y\cot(y)=x\mathop\implies^?\frac1{\sec^2(y)-x}=\int_0^\...
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Solving system of equations for trig problem in Wolfram Alpha
I'm new to Wolfram Alpha. I'm trying to learn how to do solving using a basic trig system of equations but I don't understand the ouput.
The problem is stated in graphic below, I want to solve for t ...
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HessianMatrix (norm[2](x)) in Wolfram
I'm very new to Wolfram-alpha. I'm trying to compute the Hessian Matrix of ||x|| where x is a vector. I tried this command HessianMatrix (norm[2][x]) in mathematica 13 where I use Wolframalpha input ...
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Why is $i$ here?
So I was trying to put $$\sum_{n=2}^\infty\frac{(-1)^n}{\pi(n)}$$(where $\pi(n)$ is the prime counting function) into Wolfram Alpha. It didn't work. So I decided to replace $\pi(n)$ with $\ln n$. I ...
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Why wolfram alpha is not showing integrand error?
$\tanh^{-1}$ of any real number whose modulus is $1$ or greater than $1$ is meaningless. So the following double integral must be meaningless. But when I computed the following double integral in ...
- 536
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What does italic i mean in integral calculator?
In Wolfram Alpha I computed the following double integral:
What does $i$ mean here? Does the result have imaginary part also?
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I have a sum which I can really easily show to be convergent, but Wolfram Alpha says it diverges. Is this a bug in Wolfram or is my proof flawed?
The sum is extremely simple: $\sum_{n=1}^\infty \frac{1}{n^{2+(\cos{n})^2}}$.
The proof of convergence is elementary and is as follows:
Since $(\cos{n})^2 \geq 0$ for all positive $n$, we have $0<\...
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Equation solution to absolute value in wolfram is different
The goal is to find the solution to the equation:
log(|(x^2 - x - 1) / (x^2 + x - 2)|) = 0
where log is the common logarithm.
I get x = 1/2, ±√(3/2)
Wolfram gets something much more complicated:
Here
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Difference between wolframalpha.com and tio.run/#mathematica
While solving the equation rx+(1-r)(1-x)=1/2 on wolframalpha.com returns x=1/2 as a solution, it returns error messages on tio.run/#mathematica:
...
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help with plot/equation syntax on Wolfram alpha
I'm trying to understand the syntax for making a plot on WolframAlpha.
Here's what I've entered into the type-in field. As far as I understand the documentation, it is correct.
QUESTION: can someone ...
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WolframAlpha Incorrect Result When Multiplying An Inverse By Another Matrix
According to Wolfram Alpha, $\begin{bmatrix}3 & 1 \\ 5 & 2\end{bmatrix}^{-1}\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\neq \begin{bmatrix}3 & 1 \\ 5 & 2\end{bmatrix}^{-1}$.
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Is Wolfram Alpha correct about this limit of an oscillating function?
I'm struggling with the following limit
$$\lim_{x \to \infty} e^x\big(1 + \sin(x)\big).$$
First of all I checked the solution using Wolfram. To my surprise Wolfram says that this limit exists and is ...
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Number of Vertices in a Box/Cartesian Product between Two Complete Bipartite Graph
One of my assignments needs me to create the box product between $K_{{2},{3}}$ and $K_{{1},{3}}$. After creating my own graph using standard methods. I was able to create a graph with 20 vertices ...
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Finding the $n$th derivative of $1/(1-a(1-x)(1+x))$ with respect to $x$.
I need to find the $n$th derivative of
$$\frac{1}{1-a(1-x)(1+x)}$$
with respect to $x$. Wolfram says that when $a=1$ we have the $n$th derivative as
$$\frac{1}{1-(1-x)(1+x)}^{(n)} = (-1)^n \frac{(n+1)!...
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Software to solve system of linear equations in non-standard form
Is there software to use to solve more than 4 simultaneous linear equations? Wolfram Alpha is nice but it can only do up to 4? Wolfram Alpha is nice because it can handle a non-standard form, but ...
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Help with Runge-Kutta Order 4th with a system of 3 equations
I have been trying to solve a system of equations with Runge-Kutta Order 4th but every time I try to run the program it says running but it doesn't load anything so I can't check if it is good or not. ...
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$2^x - 3^y = k$, help understanding wolfram alpha
I've been trying to understand this equation
$$2^{x} - 3^{y} = k$$
Specifically, I'm looking for all integer solutions to x and y such that k is a positive integer with $y > 1$. I figured I'd try ...
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Different 3D plot in MATLAB and Wolfram Alpha
I am trying to plot the function of two variables $f(x,y) = e^{xy}, -2 \leq x \leq 2, -1 \leq y \leq 3$ in MATLAB. Here's the code I'm using:
...
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Is WolframAlpha wrong? or am I?
Problem :
Determine a limit
$$\lim_{x\to\infty}xe^{\sin x}$$
exists or not. If it exists, find a limit.
Since $-1\le \sin x \le 1$, I can say that $\displaystyle0<\frac{1}{e}\le e^{\sin x}\le e$.
...
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Wrong wolfram alpha result for $\sin(\frac{3 \pi}{2})$ [closed]
I'm trying to compute $\sin(\frac{3 \pi}{2})$ using sin infinite product on wolfram alpha yet it gives me the answer 1 . Shouldnt the answer be -1? here is the result wolfram alpha gives me image
...
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Why does this simple continued fraction evaluate to a modified Bessel function on WolframAlpha? (without proof)
I was curious to find out the value of the first continued fraction constant $C_1$ (a non-repeating simple continuous fraction) as it obviously wouldn't be the root of a quadratic (due to it not ...
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How do I plot a gigantic function easily on WA?
I need to graph a gigantic function on WA, that has other functions inside it and some constants with preassigned values that come up a lot! For example:
W = QbBesselK...., in which Q is an equation ...
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How does Wolfram Alpha find polynomial equation of given roots?
I am experimenting with a method which will converge hopefully to a real number, for which I suspect, that it is the root of a polynomial equation. How does Wolfram Alpha find its guess?
How does WA ...
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Proof of equality given by wolfram alpha
By 'playing' with wolfram alpha and entering this sum
$$\sum_{n=0}^{+\infty}(-1)^n\left(\frac{1}{1+nx}+\frac{1}{x-1+nx}\right)$$
I found this alternative form that interest me: (since I don't know the ...
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Solve basic system of equations with two unknowns. Why solution doesn't exists? [closed]
The following equation has no solution, but I'm not sure why exactly:
$7 = 3x_1 + 5x_2 \\
13 = (1 - x_1)3 + (1 - x_2)5 + 21$
Code for Wolfram Alpha
...
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Maximum of $\frac{Bx}{x^3 + Rx + P}$
I submitted this function to Wolfram Alpha and similar tools, but none can find for me the symbolic expression for maximum value, unless I give specific values to each parameter:
$$\frac{Bx}{x^3 + Rx +...
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Numerical error in wolfram
In Wolfram Alpha, we see that $$\sum_{n=0}^\infty\frac{e^{-\pi^2n(n+1)}}{2n+1}=1$$
This is equivalent to $$\sum_{n=1}^\infty\frac{e^{-\pi^2n(n+1)}}{2n+1}=0$$
However, the last sum is impossible since ...
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Why is there a term $3.70074\times 10^{-17}x^2$ in this solution?
I was using WolframAlpha to find a polynomial of degree up to $2$ that best fits the points $(-1,2),(0,0),(1,-2),(2,-4)$. The answer I was expecting is
$$0x^2-2x+0.$$
However, here is what ...
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How to compute $ \sum_{x=y}^\infty \binom{x}{y}((1-p)(1-q))^x$?
Question
How do I compute $ \sum_{x=y}^\infty \binom{x}{y} ((1-p)(1-q))^x$? $x,y$ are integers and $p, q \in (0,1)$
Attempt
I'm trying to compute this sum to find the mixture of a geometric and ...
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Polar plot is different from rectangular plot
Here is a polar equation $r = \tan(\theta) $. I converted it into the rectangular form. This would be
$$ \sqrt{x^2 + y^2} = \frac{y}{x} $$
When I plot both in ...
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Nonsense matrix multiplication defaults in WolframAlpha
I just realized WolframAlpha arbitrarily decides which way to multiply matrices based on seemingly irrelevant stuff, and I'd like to understand whether the issue is with my knowledge of what's ...
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Find the maximum value of:$3\sqrt[3]{\dfrac{c^2-3a^2}{6}}-2\sqrt{\dfrac{a^2+b^2+c^2-ab-bc-ca}{3}}$
Let $a,b,c \in R$, find the maximum value of:$$3\sqrt[3]{\dfrac{c^2-3a^2}{6}}-2\sqrt{\dfrac{a^2+b^2+c^2-ab-bc-ca}{3}}$$
I have the solution:
$$5a^2+2b^2+c^2-2(ab+bc+ca)=5(a-\frac{b+c}{5})^2+\frac{1}{5}...
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Restricting Domain in Wolfram Alpha for Nested Quantifiers
Is there a way to restrict the domain to all positive integers when you're using Resolve[] on nested quantifiers in Wolfram Alpha? If so, how? If not but there is ...
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Wolfram Alpha wrong Integral
I want to evaluate the following integral:
$$\int_{-\infty}^0\frac{R}{\sqrt{x^2+R^2}^3}\mathrm{d}x$$
If I do it with the substitution $x=R\tan(\varphi)$ I get:
$$\int_{-\infty}^0\frac{R}{\sqrt{x^2+R^2}...
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Wolfram alpha gives two different answers for $\int^{\infty}_{-\infty} x \frac{1}{\pi} e^{-(\ln(x) - 0.3)^2} | \frac{1}{x}|dx$
So, I'm trying to calculate $$\int^{\infty}_{-\infty} x \frac{1}{\pi} e^{-(\ln(x) - 0.3)^2} \left| \frac{1}{x}\right|dx$$
When I input that into WA, it loads for a bit, then shows this result:
Just ...
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Matrix Power and Power Incorrect in Wolfram Alpha? [closed]
When computing the matrix \begin{bmatrix}1 & -\sqrt{3} \\ \sqrt{3} & 1\end{bmatrix} times its inverse, Wolfram Alpha produces this incorrect result. The same result happens when Power is ...
user1018264
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Beth one equal to beth two not known?
Wolfram Alpha seems to say that ($\beth_1=\beth_2$) is unknown, but i'm pretty sure that $\beth_2$ is greater than $\beth_1$ ? is this just a bug in WA or is there a way in set theory that you can ...
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Is $\frac{\partial}{\partial x} \cos{\sqrt{x^2+y^2}}$ indeterminate or zero at (0,0)?
I'd like to know what's the derivative of $f(x,y)=\cos{\sqrt{x^2+y^2}}$ at $(0, 0)$.
WolframAlpha says it is indeterminate.
However, if we apply the definition, we can actually evaluate it to zero:
$$
...
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How do I find $\frac{\mathrm{d}}{\mathrm{d}x} \int_{x}^{\infty} f(t, x) \mathrm{d} t$?
I am trying to compute the following derivative:
$$\frac{\mathrm{d}\Big(\int_{x}^{\infty} f(t, x) \mathrm{d} t\Big)}{\mathrm{d}x} \text{.}\tag{1}$$
It is straightforward to compute the following ...
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Wolfram Alpha computation of exponents
I am a bit confused by a Wolfram Alpha.
In my calculations I had a term like $x^{(3/2)}$ which I wrote as $\sqrt{x^3}$. As silly mistakes happen quite often to me, I often double check stuff like this ...
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How to solve this system of equations in Wolfram Alpha?
I want to solve
P0 + t0 * V0 + t2 * V2 == P1 + t1 * V1
for t0, t1 and t2, which are scalars, whereas the uppercase variables ...
